2. [35' marks) A social planner's objective is to establish 1:Ivhat conditions must be satised for natural resource allocation to be optimal, in the sense that the allocation maximises a social welfare function. Suppose a utilitarian social welfare function is given as: w: /; mega-ea (1} where U is the aggregate utility function in each period as a function of the level of consumption (0). Assume further that utility in each period is a concave function of C, so that U " (C) > U and U\"(C)